Question

Determine all positive integers n such that n^2 = 2^n. I got 2 and 4, are there any others?

Answer 1

nope consider 5, 5^2=25, 2^5 = 32, and since 2^n is exponential it increases at a greater rate than n^2 which is quadratic and at n=5 the exponential is larger than the quadratic , this will always be the case for larger n

Answer 2

in other words you are correct